Precipitating ordered skyrmion lattices from helical spaghetti and granular powders

Dustin A. Gilbert, Alexander J. Grutter, Paul M. Neves, Guo-Jiun Shu, Gergely Zimanyi, Brian B. Maranville, Fang-Cheng Chou, Kathryn Krycka, Nicholas P. Butch, Sunxiang Huang, and Julie A. Borchers

Phys. Rev. Materials 3, 014408 – Published 15 January 2019

Abstract

Magnetic skyrmions have been the focus of intense research due to their potential applications in ultrahigh-density data and logic technologies, as well as for the unique physics arising from their antisymmetric exchange term and topological protections. In this work we prepare a chiral jammed state in chemically disordered (Fe, Co)Si consisting of a combination of randomly oriented magnetic helices, labyrinth domains, rotationally disordered skyrmion lattices, and/or isolated skyrmions. Using small angle neutron scattering, we demonstrate a symmetry-breaking magnetic field sequence which disentangles the jammed state, resulting in an ordered, oriented skyrmion lattice. The same field sequence was performed on a sample of powdered $C u_{2} OSe O_{3}$ and again yields an ordered, oriented skyrmion lattice, despite the relatively noninteracting nature of the grains. Micromagnetic simulations confirm the promotion of a preferred skyrmion lattice orientation after field treatment, independent of the initial configuration, suggesting this effect may be universally applicable. Energetics extracted from the simulations suggests that approaching a magnetic hard axis causes the moments to diverge away from the magnetic field, increasing the Dzyaloshinskii-Moriya energy, followed subsequently by a lattice reorientation. The ability to facilitate an emergent ordered magnetic lattice with long-range orientation in a variety of materials despite overwhelming internal disorder enables the study of skyrmions even in imperfect powdered or polycrystalline systems and greatly improves the ability to rapidly screen candidate skyrmion materials.

Received 27 February 2018

DOI:https://doi.org/10.1103/PhysRevMaterials.3.014408

Physics Subject Headings (PhySH)

Magnetism Skyrmions

Noncentrosymmetric materials Noncollinear magnets Polycrystalline materials Single crystal materials

Micromagnetic modeling Small angle neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Dustin A. Gilbert^1,2,*, Alexander J. Grutter¹, Paul M. Neves³, Guo-Jiun Shu^4,5, Gergely Zimanyi⁶, Brian B. Maranville¹, Fang-Cheng Chou⁴, Kathryn Krycka¹, Nicholas P. Butch^1,3, Sunxiang Huang⁷, and Julie A. Borchers¹

¹NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
²Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
³Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, Maryland 20740, USA
⁴Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan
⁵Department of Materials and Mineral Resources Engineering, Institute of Mineral Resources Engineering, National Taipei University of Technology, Taipei 10608, Taiwan
⁶Department of Physics, University of California, Davis, Davis, California 95616, USA
⁷Department of Physics, University of Miami, Miami, Florida 33146, USA

^*dagilbert@utk.edu

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Vol. 3, Iss. 1 — January 2019

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Images

Figure 1
(a) Diagram of SANS measurement setup. SANS patterns for (Fe, Co)Si initially aligned with the $H ∥ [100]$ axis measured (b) with $n^{0} ∥ [100]$ and (c) $n^{0} ∥ [010]$ . SANS patterns with $H ∥ n^{0}$ rotating the sample in the (001) plane by $ϕ =$ (d) $45^{\circ}$ , (e) $67 . 5^{\circ}$ , (f) $90^{\circ}$ , then (g) back to the initial orientation $(ϕ = 180^{\circ})$ .
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Figure 2
Annular averages for (a) $ϕ = 0^{\circ} - 45^{\circ}$ and (b) $ϕ = 67 . 5^{\circ} - 180^{\circ}$ . (c) The azimuthal width of the six peaks of the skyrmion phase and (d) phase fractions from the skyrmion phase and ring phase, determined from their fractional contributions to the scattering intensity.
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Figure 3
(a) Summations of radial sector averages from Figs. 1 and 1–1, taken at increments of $60^{\circ}$ with $Δ θ = \pm 3 . 5^{\circ}$ starting at $0^{\circ}$ and $30^{\circ}$ , capturing the radial distribution of the ring and skyrmion phases, respectively. Half of the data symbols are not shown for clarity. (b) Peak center and width for the sector averages of the ring and skyrmion features as a function of the sample rotation angle.
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Figure 4
SANS patterns for (Fe, Co)Si initially aligned with the $H ∥ [110]$ axis measured (a) along the [110] axis, then rotated in the (001) plane by (b) $45^{\circ}$ , (c) $90^{\circ}$ , then (d) rotated back to 0° $(ϕ = 180^{\circ})$ . (e) The azimuthal projection of the data, (f) width of the six peaks of the skyrmion phase, and (g) phase fractions from the skyrmion phase and ring phase, determined from their fractional contributions to the scattering intensity. (h) SANS pattern after saturation along the [111] axis, and rotation by (i) $ϕ = 90^{\circ}$ and (j) $ϕ = 180^{\circ}$ .
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Figure 5
SANS patterns from powdered $C u_{2} OSe O_{3}$ taken at (a) $ϕ = 0^{\circ}$ , (b) $360^{\circ}$ , (c) $720^{\circ}$ , and (d) $1440^{\circ}$ . Azimuthal projections of the (e) $ϕ = 0^{\circ}$ , (f) $720^{\circ}$ , and (g) $1440^{\circ}$ , obtained at $q = 0.11 \pm 0.035 n m^{- 1}$ .
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Figure 6
OOMMF simulation results: (a) magnetic configuration as seen at the bisection of the cylindrical grain, under increasing $ϕ (i - v)$ , with red indicating the magnetization into the page, and blue indicating out of the page. Left and center columns show the skyrmion lattice with initial orientations $(t = 0)$ of $θ = 30^{\circ}$ and $0^{\circ}$ , respectively. The lattice is shown from the $x$ axis $(ϕ = 0^{\circ} - 45^{\circ}, ϕ = 135^{\circ} - 180^{\circ})$ or $y$ axis $(ϕ = 56^{\circ} - 124^{\circ})$ to minimize parallax, as shown in the illustrative diagrams; images are $306 nm \times 150 nm$ . Right column shows the magnetization viewed from the direction orthogonal to the plane of rotation; images are $306 nm \times 306 nm$ . (b) Orientation $θ$ of the skyrmion lattice extracted from the magnetization plots and (c) magnetic energies versus $ϕ$ . Similarly, (d) the magnetic configuration and (e) skyrmion lattice orientation and (f) magnetic energies are plotted versus $ϕ$ for a parallelepiped-shaped grain.
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